Yukawa Unification and Sparticle Spectroscopy in Gauge Mediation Models

0.78 MB·English

by  Ilia Gogoladze

UH-511-1241-15
Yukawa Unification and Sparticle Spectroscopy in
Gauge Mediation Models
Ilia Gogoladze∗1, Azar Mustafayev†2, Qaisar Shafi∗3 and Cem Salih U¨n(cid:5)4
∗Bartol Research Institute, Department of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA
†Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA
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1 (cid:5)Department of Physics, Uluda˜g University, TR16059 Bursa, Turkey
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We explore the implications of t-b-τ (and b-τ) Yukawa coupling unification condi-

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tion on the fundamental parameter space and sparticle spectroscopy in the minimal
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p gauge mediated supersymmetry breaking (mGMSB) model. We find that this sce-
p- nario prefers values of the CP-odd Higgs mass mA (cid:38) 1 TeV, with all colored sparticle
e masses above 3 TeV. These predictions will be hard to test at LHC13 but they may
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be testable at HE-LHC 33 TeV or a 100 TeV collider. Both t-b-τ and b-τ Yukawa
[
coupling unifications prefer a relatively light gravitino with mass (cid:46) 30 eV, which
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makes it a candidate hot dark matter particle. However, it cannot account for more
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0 than 15% of the observed dark matter density.
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1E-mail: [email protected];
On leave of absence from Andronikashvili Institute of Physics, Tbilisi, Georgia.
2E-mail: [email protected]
3E-mail: shafi@bartol.udel.edu
4E-mail: [email protected]
1 Introduction
TheapparentunificationoftheStandardModel(SM)gaugecouplingsatthescaleM (cid:39)
GUT
2×1016 GeVinthepresenceoflowscalesupersymmetry(SUSY)[1]isnicelyconsistentwith
supersymmetric grand unified theories (GUTs), but it does not significantly constrain the
sparticle spectrum. On the other hand, imposing t-b-τ Yukawa coupling unification (YU)
condition at M [2] can place significant constraints on the supersymmetric spectrum in
GUT
order to fit the top, bottom and tau masses [3, 4, 5]. Most work on t-b-τ YU condition has
beenperformedintheframeworkofgravitymediationSUSYbreaking[6]. Somewellknown
choices for GUT-scale boundary conditions on the soft supersymmetry breaking (SSB)
terms yield, with t-b-τ YU condition, quite severe constraints on the sparticle spectrum [3,
4, 5, 7, 8], which is further exacerbated after the discovery of the SM-like Higgs boson with
mass m (cid:39) 125−126 GeV [9, 10].
h
Models with gauge mediated SUSY breaking (GMSB) provide a compelling resolution
of the SUSY flavor problem, since the SSB terms are generated by the flavor blind gauge
interactions [11, 12, 13]. In both the minimal [11] and general [13] GMSB scenarios, the
trilinearSSBA-termsarerelativelysmallatthemessengerscale,evenifanadditionalsector
is added to generate the µ/Bµ terms [14]. Because of the small A-terms, accommodating
the light CP-even Higgs boson mass around 125 GeV requires a stop mass in the multi-TeV
range. This, in turn, pushes the remaining sparticle mass spectrum to values that are out
of reach of the 14 TeV LHC [15, 16]. There is hope, however, that the predictions can be
tested at 33 TeV High-Energy LHC (HE-LHC). This tension between the Higgs mass and
the sparticle spectrum can be relaxed if we assume the existence of low scale vector-like
particles that provide significant contribution to the CP-even Higgs boson mass [17, 18].
We will not consider this possibility here.
In this paper we investigate YU in the framework of minimal GMSB (mGMSB) sce-
nario. Here, the decoupled messenger fields generate SSB terms of particular non-universal
pattern. We know from previous studies in gravity mediation SUSY breaking scenarios
that non-universal SSB terms are necessary to achieve successful YU [5]. Moreover, be-
low M , the mGMSB model contains messenger fields that modify the evolution of the
GUT
gauge and Yukawa couplings, thereby affecting YU. We consider mGMSB in which the
messenger fields reside in 5 + ¯5 of SU(5), which is the simplest scenario that preserves
unification of the MSSM gauge couplings. We note that previous studies of mGMSB only
considered evolution below the messenger scale, which is usually much lower than M ,
GUT
and therefore could not address the question of YU.
The remainder of this paper is organized as follows. In Section 2 we briefly outline
the mGMSB framework that we use for our analysis. We describe our scanning procedure
along with the experimental constraints we applied in Section 3. In Section 4 we present
our results, focusing in particular on the sparticle mass spectrum. The table in this section
presents some benchmark points which summarize the prospects for testing these predic-
tions at the LHC. Our conclusions are presented in Section 5. In Appendix A, we briefly
discuss the renormalization group equations (RGEs) from the messenger scale to M .
GUT
1
2 Minimal Gauge Mediation
In GMSB models supersymmetry breaking is communicated from a hidden sector to the
superpartners of SM particles via some messenger fields [12]. In the minimal version, the
messengersinteractwiththevisiblesectoronlyviaSMgaugeinteractionsandtothehidden
sectorthroughanarbitraryYukawacoupling. Thetheoryisdescribedbythesuperpotential
ˆ ¯
W = W +λSΦΦ, (1)
MSSM
ˆ
where W is the usual superpotential of MSSM, S is the hidden sector gauge singlet
MSSM
¯
chiral superfield, and Φ, Φ are the messenger fields. In order to preserve perturbative gauge
coupling unification, the messenger fields are usually taken to form complete vector-like
multiplets of SU(5). Thus one could have N (1 to 4) pairs of 5 + ¯5, or a single pair of
5
10+10, or the combination 5+¯5+10+10. For simplicity, we only consider the case with
N (one to four) pairs of 5+¯5 vector-like multiplets.
5
ˆ
ThesingletfieldS developsnon-zeroVEVsforbothitsscalarandauxiliarycomponents,
(cid:68) (cid:69)
Sˆ = (cid:104)S(cid:105)+θ2(cid:104)F(cid:105),fromthehiddensectordynamics. Thisresultsinmassesforthebosonic
and fermionic components of the messenger superfields,
(cid:114)
Λ
m = M 1± , m = M , (2)
b mess f mess
M
mess
where M = λ(cid:104)S(cid:105) is the messenger scale, and Λ = (cid:104)F(cid:105)/(cid:104)S(cid:105) sets the scale of the SSB
mess
terms. Note that (cid:104)F(cid:105) < λ(cid:104)S(cid:105)2 to avoid tachyonic messengers, and in many realistic cases
(cid:104)F(cid:105) (cid:28) λ(cid:104)S(cid:105)2.
¯
Below the messenger scale M , the fields Φ and Φ decouple generating SSB masses
mess
for MSSM fields. The masses of the MSSM gauginos are generated at M from 1-loop
mess
diagrams with messenger fields. In the approximation (cid:104)F(cid:105) (cid:28) λ(cid:104)S(cid:105)2, the gaugino masses
are given by
α
i
M (M ) = N Λ, (3)
i mess 5
4π
where i = 1,2,3 stand for U(1) , SU(2) and SU(3) sectors, respectively. Since the
Y L c
MSSM scalars do not couple directly to the messengers, their SSB masses are induced at
two loop level:
3
(cid:88) (cid:16)α (cid:17)2
m2(M ) = 2N Λ2 C (φ) i , (4)
φ mess 5 i 4π
i=1
where C (φ) is the appropriate quadratic Casimir associated with the MSSM scalar field
i
φ.
The trilinear A-terms only arise at two-loop level, and thus are vanishing at the messen-
ger scale. However, they are generated below the messenger scale from the RGE evolution.
The bilinear SSB term also vanishes at M , although it is often ignored. We do not
mess
impose the relation B = 0, anticipating that the value needed to achieve the electroweak
symmetry breaking (EWSB) can be explained by some other mechanism operating at the
messenger scale [14].
The mGMSB spectrum is therefore completely specified by the following set of param-
eters:
M , Λ, N , tanβ, sign(µ), c , (5)
mess 5 grav
2
where tanβ is the ratio of the two MSSM Higgs doublet VEVs. The magnitude of µ is
determined by EWSB condition at the weak scale. The parameter c (≥ 1) affects the
grav
decay rate of the sparticles into gravitino, but it does not affect the MSSM spectrum, and
we set it equal to unity.
It is worth noting that the gaugino masses in mGMSB are non-universal at the mes-
senger scale (if M < M ). However, identical relations at the same scale among the
mess GUT
gauginos can be obtained through RGE evolution in the gravity mediated SUSY breaking
framework starting with universal gaugino masses at M . On the other hand, Eq. (4)
GUT
implies a universal SSB mass terms for the up (H ) and down (H ) Higgs doublets at the
u d
messenger scale. Within the gravity mediated framework this relation can be obtained
at the same scale if one imposes non-universal Higgs masses m2 < m2 at M . In-
Hu Hd GUT
deed, this non-universality is a necessary condition for compatibility with t-b-τ YU in the
gravity mediation case with universal gaugino masses at M [7, 8]. However, the rela-
GUT
tion m2 < m2 is introduced by hand in gravity mediated SO(10) GUT, while t-b-τ YU
Hu Hd
in mGMSB can be achieved without such ad hoc conditions, as we will see later. From
Eq. (4) the sfermion masses in mGMSB are non-universal at the messenger scale, but it is
not easy to find the same pattern at M within the gravity mediation scenario. Hence,
mess
the sfermion sector could be a good place to see differences between gravity and gauge
mediation SUSY breaking scenarios that are compatible with YU condition at the GUT
scale.
3 Scanning Procedure and Experimental Constraints
For our scan over the fundamental parameter space of mGMSB, we employed ISAJET 7.84
package [19] that we modified to include the RGE evolution above M in MSSM with
mess
N pairs of 5 + ¯5 messengers. In this package, the weak-scale values of gauge and third
5
generation Yukawa couplings are evolved from M to M via the MSSM RGEs in the
Z mess
DR regularization scheme. Above M the messenger fields are present, which changes
mess
the beta-functions for the SM gauge and Yukawa couplings. The modified RGEs between
M and M are given in Appendix A. M is defined as the scale at which g = g
mess GUT GUT 1 2
and is approximately equal to 2 × 1016 GeV, the same as in MSSM. We do not strictly
enforce the unification condition g = g = g at M , since a few percent deviation
3 1 2 GUT
from unification can be accounted by unknown GUT-scale threshold corrections [20]. For
simplicity, we do not include the Dirac neutrino Yukawa coupling in the RGEs, whose
contribution is expected to be small.
The SSB terms are induced at the messenger scale and we set them according to ex-
pressions (3) and (4). From M the SSB parameters, along with the gauge and Yukawa
mess
couplings, are evolved down to the weak scale M . In the evolution of Yukawa cou-
Z
plings the SUSY threshold corrections [21] are taken into account at the common scale
√
M = m m , wherem andm denote thesoft masses of theleft and right-handed
SUSY t˜L t˜R t˜L t˜R
top squarks. The entire parameter set is iteratively run between M and M using the
Z GUT
full 2-loop RGEs until a stable solution is obtained. To better account for leading-log cor-
rections, one-loopstep-betafunctionsareadoptedforthegaugeandYukawacouplings, and
the SSB parameters m are extracted from RGEs at multiple scales: at the scale of its own
i
mass, m = m (m ), for the unmixed sparticles, and at the common scale M for the
i i i SUSY
mixed ones. The RGE-improved 1-loop effective potential is minimized at M , which
SUSY
3
effectively accounts for the leading 2-loop corrections. Full 1-loop radiative corrections [21]
are incorporated for all sparticle masses.
We have performed random scans over the model parameters (5) in the following range:
103 GeV ≤ Λ ≤ 107 GeV,
105 GeV ≤ M ≤ 1016GeV,
mess
40 ≤ tanβ ≤ 60, (6)
N = 1, µ < 0.
5
Varying N from 1 to 4, we find that the low scale sparticle spectrum does not change
5
significantly [15]. Thus we present results only for N = 1 case. Regarding the MSSM
5
parameter µ, its magnitude but not its sign is determined by the radiative electroweak
symmetry breaking. In our model we set sign(µ) = −1. A negative µ-term together with
a positive gaugino mass M gives negative contribution to the muon anomalous magnetic
2
moment calculation [22] which would disagree with the measured value for muon g−2 [23].
This, however, is not a problem, since the sparticle spectrum is quite heavy in our scenario.
As we will see, the smuons are often heavier than 1 TeV. Hence, the SUSY contribution
to muon g −2 is not significant, which also is the case in t-b-τ YU scenarios [24, 5]. On
the other hand, a negative sign of µ with positive signs for all gauginos helps to realize
YU. The reason for this is that in order to implement YU, we require significant SUSY
threshold corrections to the bottom quark Yukawa coupling. One of the dominant finite
corrections is proportional to µM [25] and it helps to realize Yukawa unification if this
3
combination has negative sign [5]. Finally, we employ the current central value for the top
mass, m = 173.3 GeV. Our results are not too sensitive to one or two sigma variation of
t
m [27].
t
In scanning the parameter space, we employ the Metropolis-Hastings algorithm as
described in Ref. [28]. The data points collected all satisfy the requirement of radia-
tive electroweak symmetry breaking (REWSB). After collecting the data, we impose the
mass bounds on the particles [29] and use the IsaTools package [30, 24] to implement the
various phenomenological constraints. We successively apply mass bounds including the
Higgs [9, 10] and gluino masses [31], and the constraints from the rare decay processes
B → µ+µ− [32], b → sγ [33] and B → τν [34]. The constraints are summarized below
s u τ
in Table 1. Notice that we used wider range for the Higgs boson mass, since there is an
approximate error of around 2 GeV in the estimate of the mass that largely arises from
theoretical uncertainties in the calculation of the minimum of the scalar potential, and to
a lesser extent from experimental uncertainties in the values of m and α .
t s
123GeV ≤ m ≤ 127 GeV
h
m ≥ 1.5 TeV
g˜
0.8×10−9 ≤ BR(B → µ+µ−) ≤ 6.2×10−9 (2σ)
s
2.99×10−4 ≤ BR(b → sγ) ≤ 3.87×10−4 (2σ)
0.15 ≤ BR(Bu→τντ)MSSM ≤ 2.41 (3σ)
BR(Bu→τντ)SM
Table 1: Phenomenological constraints implemented in our study.
Following ref. [28] we define the parameters R and R which quantify t-b-τ YU and
tbτ bτ
4
b-τ YU respectively:
Max(y ,y ,y ) Max(y ,y )
t b τ b τ
R = , R = (7)
tbτ bτ
Min(y ,y ,y ) Min(y ,y )
t b τ b τ
Thus, R is a useful indicator for Yukawa unification with R (cid:46) 1.1, for instance, corre-
sponding to Yukawa unification to within 10%, while R = 1.0 denotes ‘perfect’ Yukawa
unification.
4 Results
Figure 1: Plots in R −Λ, R −M , M −Λ and µ−M planes. All points are
tbτ tbτ mess mess mess
consistent with REWSB. Green points also satisfy mass bounds and B-physics constraints.
Red points are a subset of green and they are compatible with t-b-τ YU. In the top panels
regions below the horizontal line are compatible with YU such that R ≤ 1.1
tbτ
.
Figure 1 displays the regions in the parameter space that are compatible with t-b-τ
YU with plots in R −Λ, R −M , M −Λ and µ−M planes. All points are
tbτ tbτ mess mess mess
consistent with REWSB. Green points satisfy the mass bounds and B-physics constraints.
Red points are a subset of green ones and they are compatible with t-b-τ YU. In the top
panelsthedashedlineindicatestheregionconsistentwithYUwithR ≤ 1.1. TheR −Λ
tbτ tbτ
plane shows that the parameter Λ in mGMSB is constrained by 105GeV (cid:46) Λ (cid:46) 106 GeV
for t-b-τ YU with R ≤ 1.1. As seen from the R − M plane, YU imposes a far
tbτ tbτ mess
less stringent constraint on M , namely 108GeV (cid:46) M (cid:46) 1014 GeV. We also present,
mess mess
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Figure 2: Plots in R −tanβ and R −tanβ planes. The color coding is the same as in
tbτ bτ
Figure 1.
Figure 3: Plots in m − tanβ plane for t-b-τ YU (left panel) and b-τ YU (right panel).
h
The color coding is the same as in Figure 1 except the Higgs mass bound is not applied in
these panels.
for additional clarity, the results in M −Λ plane. The MSSM parameter µ lies in the
mess
range −8TeV (cid:46) µ (cid:46) −3 TeV for compatibility with YU. We see that there are plenty of
solutions consistent with the mass bounds and constraints from rare B-decays. However,
only the thin red stripe is compatible with YU.
Thestrongimpactoft-b-τ YUonthefundamentalparameterspaceissomewhatrelaxed
if only b-τ YU is imposed. Figure 2 shows the differences between t-b-τ and b-τ YU cases
with plots in R − tanβ and R − tanβ planes. The color coding is the same as in
tbτ bτ
Figure 1. One sees that, t-b-τ YU only allows a very narrow range for tanβ, namely
54 (cid:46) tanβ (cid:46) 60, and perfect t-b-τ YU consistent with the experimental constraints can
be realized when tanβ ≈ 56. On the other hand, the R − tanβ plane shows that the
bτ
range for tanβ is slightly enlarged, 50 (cid:46) tanβ (cid:46) 60, with b-τ YU, and perfect b-τ YU is
obtained for 54 (cid:46) tanβ (cid:46) 57.
A similar comparison based on the range for the SM-like Higgs boson mass is given in
Figure 3 with plots in m − tanβ planes for t-b-τ (left panel) and b-τ (right panel) YU
h
cases. The color coding is the same as in Figure 1, except that the Higgs mass bound is
not applied in these panels. The left panel shows that demanding 10% or better YU, the
lightest CP-even Higgs boson mass can be m ≈ 119−125 GeV for t-b-τ case, while it can
h
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Figure 4: Plots in m −m , m −m , m −m and m −m planes. The color coding
t˜1 t˜2 u˜L g˜ τ˜1 τ˜2 χ˜±1 χ˜01
is the same as in Figure 1.
Figure 5: Plots in M −m , Λ−m , R −m and R −m planes. The color coding
mess G˜ G˜ tbτ G˜ bτ G˜
is the same as in Figure 1.
be as light as 117 GeV in the case of b-τ YU, as shown in the right panel. The panels of
Figure 3 highlight how stringent the Higgs boson mass constraint is on the fundamental
parameter space of mGMSB compatible with YU. The left panel shows that the 125 GeV
Higgs boson mass and t-b-τ YU more or less equivalently constrain the parameter space.
On the other hand, as seen from the right panel, b-τ YU can be realized for tanβ (cid:38) 40,
while the mass bound on the Higgs boson excludes the region with tanβ (cid:46) 50.
Figure4displaysthemassspectrumofsupersymmetricparticlesinm −m , m −m ,
t˜2 t˜1 u˜L g˜
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Point 1 Point 2 Point 3 Point 4 Point 5
Λ 0.94×106 1.51×106 7.6×105 4.7×105 1.16×106
M 1.5×1014 1.3×1014 1.2×108 8.6×1013 1.3×1015
mess
tanβ 56.1 59.3 58.7 54.8 52.7
µ -4906 -6727 -2995 -4268 -3984
A -3564 -5479 -1933 -1834 -4513
t
A -3600 -5540 -1946 -1891 -4868
b
A -268.1 -462.9 -123.2 -140.4 -535.1
τ
m 124 125 123 123 124
h
m 1148 1640 929 1665 2378
H
m 1141 1629 923 1654 2363
A
m 1153 1643 934.2 1668 2380
H±
m 1305, 2438 2098, 3868 1045, 1971 654, 1249 1602, 2960
χ˜0
1,2
m 4902, 4903 6725, 6725 3001, 3002 4190, 4190 3993, 3995
χ˜0
3,4
m 2440, 4902 3871, 6724 1972, 3002 1251, 4154 2961, 3996
χ˜±
1,2
m 6113 9350 4995 3372 7178
g˜
m 9545, 8590 13434, 12152 6903, 6469 8140, 7206 7818, 7255
u˜L,R
m 6325, 7784 9152, 11112 5569, 6186 5011, 6515 5752, 6745
t˜1,2
m 9545, 8317 13434, 11796 6903, 6412 8140, 6937 7819, 7124
d˜L,R
m 6280, 7743 9134, 11053 5617, 6148 5054, 6482 6022, 6709
˜b1,2
m 5181 7122 2727 4659 3560
ν˜e,µ
m 4843 6625 2659 4358 3372
ν˜τ
m 5186, 3698 7129, 5044 2735, 1478 4663, 3324 3567, 2378
e˜L,R
m 2600, 4845 3397, 6628 1193, 2667 2340, 4357 1748, 3381
τ˜1,2
R 1.00 1.09 1.09 1.06 1.23
tbτ
R 1.00 1.08 1.06 1.02 1.07
bτ
Table 2: Benchmark points for exemplifying our results. All masses and scales are given
in GeV units. Point 1 depicts a solution with perfect YU. Point 2 shows a solution with
125 GeV mass for h consistent with YU. Point 3 displays a solution with essentially the
lowest stau mass consistent with YU. Similarly, point 4 shows essentially the lightest mass
forthelightestneutralino. Thispointalsodemonstratesthelightestgluinoandstopmasses
obtained from our scans. Point 5 displays a solution which is compatible with b-τ YU, but
not with t-b-τ YU.
m −m andm −m planes,withthecolorcodingthesameasinFigure1. Asseenfrom
thτ˜e2topτ˜p1anels, tχh˜±1e coloχ˜r01ed sparticles are quite heavy. Thus t-b-τ YU requires m (cid:38) 4 TeV.
t˜1
Since the SSB trilinear scalar interaction term A is relatively small [15], the heavier stop is
t
expected to be about the same mass ((cid:38) 4 TeV) as the lighter stop. Similarly, the squarks
of the first two families and the gluino have masses in the few TeV range. The m −m
q˜L g˜
plane shows that m (cid:38) 3 TeV and m (cid:38) 6 TeV for consistency with t-b-τ YU as well as
g˜ q˜L
the experimental constraints.
The bottom panels of Figure 4 display the mass spectra for the lightest sparticles which
are found to be stau, chargino and neutralino. According to the m −m panel, τ˜ can
τ˜2 τ˜1 1
be as light as 1 TeV, while m (cid:38) 2 TeV. Similarly, the m − m plane displays the
masses of the lightest charginoτ˜a2nd neutralino with the latterχ˜±1(cid:38) 600χ˜G01eV, and the former
(cid:38) 1200 GeV.
Finally, Figure 5 displays the gravitino mass, m , in R −m and R −m planes
G˜ tbτ G˜ bτ G˜
with the color coding as in Figure 1. As is well-known, the gravitino is usually the LSP
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in the mGMSB framework, and its mass can be as heavy as 10 TeV. A light gravitino is a
plausible dark matter candidate and it can also manifest itself through missing energy in
colliders [36].
In the standard scenarios, the relic density bound (Ωh2 (cid:39) 0.11 [35]) is satisfied with
a gravitino mass ∼ 200 eV [36], which makes it a hot dark matter candidate. The hot
component of dark matter, however, cannot be more than 15% which, in turn, implies that
the gravitino mass should be less than about 30 eV [36]. This indeed is predicted from
Figure 5. The panels of Figure 5 represent the impact of YU on the gravitino mass. Both
t-b-τ and b-τ YU do not allow a gravitino that is too heavy, preferring instead a gravitino
lighter than 100 eV or so. The R − m plane shows that t-b-τ YU is mostly realized
tbτ G˜
with m (cid:46) 30 eV, with essentially perfect YU possible for nearly massless gravitinos. The
G˜
bound on the gravitino mass is not significantly relaxed for b-τ YU. However, essentially
perfect YU is found for m (cid:46) 50 eV. In order to have a complete dark matter scenario one
G˜
could invoke axions as cold dark matter.
In Table 2 we present five benchmark points that exemplify our results. The points are
chosen to be consistent with the experimental constraints and YU. The masses are given
in GeV. Point 1 depicts a solution with perfect YU. Point 2 shows the heaviest mass in our
scan for the lightest CP-even Higgs boson, while point 3 displays the lightest stau mass
that we found, consistent with YU. Similarly, point 4 represents the lightest neutralino
mass foundin our scan. This point also shows the lightest gluino and stop masses that we
obtained. Point 5 displays a solution which is compatible with b-τ YU, but not with t-b-τ
YU.
5 Conclusion
Models based on the gauge mediated SUSY breaking are highly motivated, as they provide
an atractive solution to the SUSY flavor problem. We have explored the implications
of t-b-τ and b-τ YU condition on the sparticle spectroscopy in the framework of mGMSB
wherethemessengersresidein5+¯5multipletsofSU(5)andonlyinteractwithvisiblesector
viagaugeinteractions. WefindthatYUleadstoaheavysparticlespectrumwiththelowest
masssparticlesbeingthelightestneutralino(m (cid:38) 600GeV),chargino(m (cid:38) 1200GeV)
χ˜0 χ˜±
and stau (m (cid:38) 1000 GeV). In addition, YU p1refers values of the CP-od1d Higgs boson
τ˜
mass m to be greater than 1 TeV and all colored sparticle masses above 3 TeV. Such
A
heavy sparticles can escape detection at the 13-14 TeV LHC, but should be accessible at
HE-LHC 33 TeV or the proposed 100 TeV collider. We find that YU requirement in the
mGMSB framework leads to a spectrum of gauginos, Higgses and staus, that is very similar
to the one in gravity mediated SO(10) GUT, although for different reasons. The details
of the rest of sfermion spectrum are different, but they are at about the same heavy scale.
However, YU in mGMSB framework does not require any ad hoc assumptions, such as as
SSB non-universalities that are necessary in gravity mediated GUTs. It is also interesting
to note that t-b-τ and b-τ YU favor a gravitino mass less than 30 eV, which makes it a hot
dark matter candidate. In this case, the gravitino cannot comprise more than 15% of the
dark matter density, and one may invoke axions in order to have a complete dark matter
scenario.
9